The present paper includes the local and semilocal convergence analysis of a fourth-order method based on quadrature formula in Banach spaces. weaker hypotheses used are only first Fréchet derivative. new approach provides residual errors, number iterations, radii, expected order convergence, estimates uniqueness solution. Such not provided approaches using Taylor expansions involving higher-or...

This article makes use of simultaneous decomposition four quaternion matrixes to investigate some Sylvester-like matrix equation systems. We present useful necessary and sufficient conditions for the consistency system equations in terms equivalence form block matrixes. also derive general solution according partition coefficient As an application system, we practical a ϕ-Hermitian provide when...

We compare the convergence balls and dynamical behaviors of two efficient weighted-Newton-like equation solvers by Sharma Arora, Grau-Sánchez et al. First all, results ball for these algorithms are established employing generalized Lipschitz constants assumptions on first derivative only. Consequently, outcomes radii convergence, measurable error distances existence–uniqueness areas solution di...